Adding a converter to Binding="{Binding}" - wpf

Question

I have a DataGridColumnHeader Style that has a TextBox situated above the DataGridColumn. In the TextBox Style, there is a DataTrigger that sets its visibility based on the Text in the DataGridColumn. Rather than checking if its value equals "Pos", I would like to use a converter to see if its value begins with the string "Pos". But when I add the converter, the value parameter in the converter turns out not being a string. Instead it is the MainWindow object that the datagrid belongs to. Why would it take on a different meaning when I add a converter?
<Style TargetType="{x:Type DataGridColumnHeader}" x:Key="DataGridColumnHeaderStyle"
xmlns:theme="clr-namespace:Microsoft.Windows.Themes;assembly=PresentationFramework.Aero">
<Style.Resources>
<SolidColorBrush x:Key="borderBackground">#E4E5ED</SolidColorBrush>
</Style.Resources>
<Setter Property="Template">
<Setter.Value>
<ControlTemplate TargetType="{x:Type DataGridColumnHeader}">
<Border Background="{StaticResource borderBackground}">
<Grid>
<Grid.ColumnDefinitions>
<ColumnDefinition />
</Grid.ColumnDefinitions>
<Grid.RowDefinitions>
<RowDefinition />
<RowDefinition />
</Grid.RowDefinitions>
<TextBox Margin="1" Grid.Column="0" Grid.Row="0" IsReadOnly="True"
Text="{Binding Path=DataContext.TotalPos, StringFormat=N0, Mode=OneWay, RelativeSource={RelativeSource FindAncestor, AncestorLevel=1, AncestorType={x:Type DataGrid}}}">
<TextBox.Style>
<Style TargetType="TextBox">
<Setter Property="Visibility" Value="Hidden"/>
<Style.Triggers>
<DataTrigger Binding="{Binding}" Value="Pos">
<Setter Property="Visibility" Value="Visible"/>
</DataTrigger>
</Style.Triggers>
</Style>
</TextBox.Style>
</TextBox>
<theme:DataGridHeaderBorder Grid.Column="0" Grid.Row="1" SortDirection="{TemplateBinding SortDirection}"
IsHovered="{TemplateBinding IsMouseOver}"
IsPressed="{TemplateBinding IsPressed}"
IsClickable="{TemplateBinding CanUserSort}"
Background="{TemplateBinding Background}"
BorderBrush="{TemplateBinding BorderBrush}"
BorderThickness="{TemplateBinding BorderThickness}"
Padding ="{TemplateBinding Padding}"
SeparatorVisibility="{TemplateBinding SeparatorVisibility}"
SeparatorBrush="{TemplateBinding SeparatorBrush}">
<TextBlock Grid.Column="0" Grid.Row="1" Text="{TemplateBinding Content}"
SnapsToDevicePixels="{TemplateBinding SnapsToDevicePixels}"
VerticalAlignment="{TemplateBinding VerticalContentAlignment}"
HorizontalAlignment="{TemplateBinding HorizontalContentAlignment}"
TextWrapping="Wrap"></TextBlock>
</theme:DataGridHeaderBorder>
<Thumb Grid.Column="0" Grid.Row="1" Name="PART_LeftHeaderGripper" HorizontalAlignment="Left" Style="{StaticResource ColumnHeaderGripperStyle}"/>
<Thumb Grid.Column="0" Grid.Row="1" Name="PART_RightHeaderGripper" HorizontalAlignment="Right" Style="{StaticResource ColumnHeaderGripperStyle}"/>
</Grid>
</Border>
</ControlTemplate>
</Setter.Value>
</Setter>
</Style>
With converter:
<src:StartsWith x:Key="startsWith"/>
...
<Style TargetType="TextBox">
<Setter Property="Visibility" Value="Hidden"/>
<Style.Triggers>
<DataTrigger Binding="{Binding Converter={StaticResource startsWith}, ConverterParameter=Pos}" Value="True">
<Setter Property="Visibility" Value="Visible"/>
</DataTrigger>
</Style.Triggers>
</Style>
...
[ValueConversion(typeof(string), typeof(bool))]
public class StartsWith : IValueConverter
{
public object Convert(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
{
return ((string)value).StartsWith((string)parameter);
}
public object ConvertBack(object value, Type targetType, object parameter, System.Globalization.CultureInfo culture)
{
throw new Exception("Not Implemented.");
}
}

Answer 1

It doesn't know what to bind to...add Binding RelativeSource={RelativeSource Self}, Path=Text for the converter.

Answer 2

I bind with this, thanks
<DataTrigger Binding="{Binding RelativeSource={RelativeSource FindAncestor, AncestorType=DataGridColumnHeader, AncestorLevel=1}, Path=Column.Header, Converter={StaticResource startsWith}, ConverterParameter=Pos}" Value="True">